Unformatted text preview: CS 188 Fall 1993 Introduction to AI Stuart Russell Midterm 2 You have 1 hour, 20 minutes. The exam is open-book, open-notes. You will not necessarily nish all questions, so do your best ones rst. Write your answers in blue books. Hand them all in. 60 points total. Panic not.
1. (14 pts.) Situation calculus and In this question we will investigate the relationship between strips action schemata and situation calculus descriptions of actions. (a) (6 pts) Translate the following situation calculus axioms into one or more STRIPS action schemata: 8sxpEdible(x) ^ Holding(p x s) ) Inside(x p Result(Eat(p x) s)) 8sxpEdible(x) ^ Holding(p x s) ) :Holding(p x Result(Eat(p x) s)) 8sxypHolding(p y s) ^ y 6= x , Holding(p y Result(Eat(p x) s)) 8sxypInside(y p s) ) Inside(y p Result(Eat(p x) s)) 8sxyp:Inside(y p s) ^ y 6= x ) :Inside(y p Result(Eat(p x) s)) (b) (2 pts) Are there any frame axioms missing from the above set of axioms? (c) (6 pts) Translate the following STRIPS action schema into one or more situation calculus axioms (including all necessary frame axioms): Action : Barf (p x) Preconds : Inside(x p)] AddList : ] DeleteList : Inside(x p)] strips 2. (10 pts.) Nonlinear planning
~h Consider the following partially-ordered plan (a step followed by e.g. ~g means that the steps deleted g):
h C g Finish E ~g ~h F ~g ~h (a) (b) (c) (d) (2 pts) How many possible linearizations does the plan have? h (2 pts) Which steps possibly threaten B ;!C ? h (2 pts) Which steps necessarily threaten B ;!C ? (2 pts) How can the plan be re ned (by a standard partial-order planner) to remove a possible threat to h B ;!C ? (e) (2 pts) Is g necessarily true at the nish step? 3. (7 pts.) Basic probability In this question we consider a set of n Boolean random variables X1 : : :Xn . Suppose that the joint distribution for X1 : : :Xn is uniform (all entries identical). 1 (a) (3 pts) What can you deduce about P(Xi)? (b) (2 pts) Is it necessarily the case that P(Xi jXj ) = P(Xi ) for all i, j ? (c) (2 pts) What is the value of each entry in the joint?
4. (13 pts.) Independence in networks
A A Consider the following four networks, constructed by introducing the nodes in the order A, B, C:
B A A B B C C C B C i) ii) iii) iv) (a) (10 pts) For each of the following statements, say whether it necessarily holds in each of the networks (draw a 4 4 table with 1,2,3,4 down the left-hand side and i, ii, iii, iv across the top, and ll in a Y in the boxes where the statement holds): 1 P(C jA B ) = P(C jA) 2 P(C jA B ) = P(C jB ) 3 P(B jA) = P(B ) 4 P(B C jA) = P(B jA)P(C jA) (b) (3 pts) True/false: It is possible to construct a network topology connecting A, B, C for which it is necessarily false that P(AjC ) = P(A).
5. (16 pts.) Belief network design Consider the following random variables, pertaining to driving home after a New Year's Eve party in Lake Tahoe: BrakeFailure | whether your brakes fail Drunk | whether you are actually over the limit AccidentSeverity | values None, FenderBender, Severe IcyWeather | whether the weather is icy Arrested | whether you get arrested Injured | whether you are injured Jailed | whether you go to jail (a) (8 pts) Pick a reasonable ordering for the variables and use it to construct a network topology. Try to minimize the amount of information required for the conditional probability tables, while respecting the obvious causal in uences in the doamin. (b) (3 pts) Label each node with the number of independent probabilities that must be supplied for the associated conditional probability table. (c) (4 pts) Give a reasonable conditional probability table associated with the Jailed node. (d) (1 pt) Is your network singly-connected? 2 ...
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